Question: What do the following two equations represent? $-4x-5y = -4$ $5x-4y = 4$
Answer: Putting the first equation in $y = mx + b$ form gives: $-4x-5y = -4$ $-5y = 4x-4$ $y = -\dfrac{4}{5}x + \dfrac{4}{5}$ Putting the second equation in $y = mx + b$ form gives: $5x-4y = 4$ $-4y = -5x+4$ $y = \dfrac{5}{4}x - 1$ The slopes are negative inverses of each other, so the lines are perpendicular.